EP 1 355 041 A2 has disclosed a turbine blade or vane of this type. The cast turbine blade has a cavity which extends from the blade root through the platform into the blade profile. The cross section of the cavity is substantially constant along its extent. The cavity is surrounded by an inner wall and has a cross section which is enlarged only in the region of the platform, by virtue of the inner wall being set back in the region of the platform. The material thickness in the transition region between blade profile and platform projecting transversely to it consequently remains constant, so that the transition between them can be cooled more successfully.